6. (a) Show, by integration, that the centre of mass of a uniform right cone, of radius \(a\) and height \(h\), is a distance \(\frac { 3 } { 4 } h\) from the vertex of the cone.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{45c51316-7d58-4c16-9b5f-1d7421060a88-5_789_914_406_486}
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\caption{Fig. 3}
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A uniform right cone \(C\), of radius \(a\) and height \(h\), has vertex \(A\). A solid \(S\) is formed by removing from \(C\) another cone, of radius \(\frac { 2 } { 3 } a\) and height \(\frac { 1 } { 2 } h\), with the same axis as \(C\). The plane faces of the two cones coincide, as shown in Fig. 3.
(b) Find the distance of the centre of mass of \(S\) from \(A\).